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Improved Integral Attack on Generalized Feistel Cipher

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Information Security and Cryptology (Inscrypt 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12020))

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Abstract

Division property is a generalized integral property proposed by Todo in Eurocrypt 2015. Utilizing automated tools such as SAT and MILP, the complexity to search for integral distinguisher by division property was greatly reduced. Based on division property and automated tools, Derbez et al. obtained a 10-round integral distinguisher of RECTANGLE by considering the linear transformation of the input and output state bits of the cipher, which is one round longer than known integral distinguishers. In this paper, we further consider improved integral attack on block ciphers with Generalized Feistel Structure (GFS cipher) by considering the linear transformation of the S-boxes. Taking the 16-branch GFS cipher with 4-bit S-boxes as an example, using this improved method, we can increase the round of integral distinguishers by one round for many S-boxes. The result implies that ability to resist this improved integral attack should also be considered when designing corresponding GFS ciphers.

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Notes

  1. 1.

    https://github.com/msoos/cryptominisat.

References

  1. Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_12

    Chapter  Google Scholar 

  2. Zhang, H., Wu, W.: Structural evaluation for generalized Feistel structures and applications to LBlock and TWINE. In: Biryukov, A., Goyal, V. (eds.) INDOCRYPT 2015. LNCS, vol. 9462, pp. 218–237. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26617-6_12

    Chapter  Google Scholar 

  3. Todo, Y.: Integral cryptanalysis on full MISTY1. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 413–432. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_20

    Chapter  Google Scholar 

  4. Todo, Y., Morii, M.: Bit-based division property and application to Simon family. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 357–377. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_18

    Chapter  Google Scholar 

  5. Boura, C., Canteaut, A.: Another view of the division property. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 654–682. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_24

    Chapter  Google Scholar 

  6. Xiang, Z., Zhang, W., Bao, Z., Lin, D.: Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 648–678. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_24

    Chapter  Google Scholar 

  7. Sun, L., Wang, W., Wang, M.: Automatic search of bit-based division property for ARX ciphers and word-based division property. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 128–157. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_5

    Chapter  Google Scholar 

  8. Eskandari, Z., Kidmose, A.B., Kölbl, S., Tiessen, T.: Finding integral distinguishers with ease. In: Cid, C., Jacobson, M.J. (eds.) SAC 2018. LNCS, vol. 11349, pp. 115–138. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-10970-7_6

  9. Derbez, P., Fouque, P.-A., Lambin, B.: Linearly equivalent S-boxes and the Division Property. Cryptology ePrint Archive, 2019/097 (2019)

    Google Scholar 

  10. Nyberg, K.: Generalized Feistel networks. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 91–104. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0034838

    Chapter  Google Scholar 

  11. Suzaki, T., Minematsu, K.: Improving the generalized Feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13858-4_2

    Chapter  Google Scholar 

  12. Cook, S.A.: The complexity of theorem-proving procedures. In: STOC 1971, pp. 151–158. ACM (1971)

    Google Scholar 

  13. Biham, E., Anderson, R., Knudsen, L.: Serpent: a new block cipher proposal. In: Vaudenay, S. (ed.) FSE 1998. LNCS, vol. 1372, pp. 222–238. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-69710-1_15

    Chapter  Google Scholar 

  14. Banik, S., et al.: Midori: a block cipher for low energy. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 411–436. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48800-3_17

    Chapter  Google Scholar 

  15. Bogdanov, A., Knežević, M., Leander, G., Toz, D., Varıcı, K., Verbauwhede, I.: spongent: a lightweight hash function. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 312–325. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23951-9_21

    Chapter  Google Scholar 

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Acknowledgements

We thank the anonymous reviewers for their careful reading of our paper and helpful comments. This research was supported by the National Natural Science Foundation of China (Nos. U1536101, 61521003) and the National cryptography Development Fund of China (Nos. MMJJ20180204, MMJJ20170103).

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Authors and Affiliations

  1. Information Engineering University, Zhengzhou, China

    Zhichao Xu & Hong Xu

  2. Shanghai Jiao Tong University, Shanghai, China

    Hong Xu & Xuejia Lai

Authors
  1. Zhichao Xu
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  2. Hong Xu
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  3. Xuejia Lai
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Correspondence to Hong Xu .

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Editors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Zhe Liu

  2. Computer Science Department, Columbia University, New York, NY, USA

    Moti Yung

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Xu, Z., Xu, H., Lai, X. (2020). Improved Integral Attack on Generalized Feistel Cipher. In: Liu, Z., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2019. Lecture Notes in Computer Science(), vol 12020. Springer, Cham. https://doi.org/10.1007/978-3-030-42921-8_28

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  • DOI: https://doi.org/10.1007/978-3-030-42921-8_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-42920-1

  • Online ISBN: 978-3-030-42921-8

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